Abstract
The Lieb-Schultz-Mattis (LSM) theorem, originally proposed in 1961, revealed a fundamental constraint on the ground states of one-dimensional quantum spin systems with half-integer spin per unit cell, SU (2) symmetry, and lattice translation invariance. It prohibits the existence of a unique, gapped ground state under these conditions. In the past decade, various extensions and generalizations of the Lieb-Schultz-Mattis (LSM) theorem have been proposed, uncovering the critical roles of symmetries such as time-reversal, ℤ2×ℤ2 spin rotations, U (1), and lattice translation. These symmetries impose strong constraints that can forbid the existence of a unique, gapped ground state.
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